Ch 7 Bonds Bond Valuation: Callaghan bonds have 10 yrs remaining to maturity. Interest is paid annually, they have a $1000 par value, the coupon interest rate is 8% and the yield to maturity is 9%. What is the bond price? A: N = 10; I/YR = YTM = 9%; PMT = 0.08 1,000 = 80; FV = 1000; PV = VB = ? PV = $935.82. Yield to maturity and future price: A bond has a $1000 par value, 10 yrs to maturity and a 7% annual coupon and sells for $985. a. What is the ield to maturity (YTM)? b. Assume the YTM remains constant for the nest 3 yrs. What will the price for 3 yrs from today? a. N = 10; PV = -985; PMT = 70; FV = 1000; YTM = ? Solve for I/YR = YTM = 7.2157% 7.22%. b. N = 7; I/YR = 7.2157; PMT = 70; FV = 1000; PV = ? Solve for VB = PV = $988.46. Bond valuation: Nung Corp. outstanding bonds have a $1000 par value a 9% semiannual coupon, 8 yrs to maturity, and a 8.5% YTM. What is the bond price? The problem asks you to find the price of a bond, given the following facts: N = 2 8 = 16; I/YR = 8.5/2 = 4.25; PMT = 45; FV = 1000. With a financial calculator, solve for PV = $1,028.60. YIELD TO MATURITY A firm’s bonds have a maturity of 10 years with a $1,000 face value, have an 8% semiannual coupon, are callable in 5 years at $1,050, and currently sell at a price of $1,100. What are their normal yield to maturity and their normal yield to call? What return should investors expect to earn on these bonds? find YTM: N = 10 2 = 20; PV = -1100; PMT = 0.08/2 1,000 = 40; FV = 1000; I/YR = YTM = ? YTM = 3.31% 2 = 6.62%. find YTC: N = 5 2 = 10; PV = -1100; PMT = 0.08/2 1,000 = 40; FV = 1050; I/YR = YTC = ? YTC = 3.24% 2 = 6.49%. Since the YTC is less than the YTM, investors would expect the bonds to be called and to earn the YTC. YIELD TO CALL It is now January 1, 2009, and you are considering the purchase of an outstanding bond that was issued on January 1, 2007. It has a 9.5% annual coupon and had a 30-year original maturity. (It matures on December 31, 2036.) There is 5 years of call protection (until December 31, 2011), after which time it can be called at 109 –that is, at 109% of par, or $1,090. Interest rates have declined since it was issued; and it is now selling at 116.575% of par, or $1,165.75. a. What is the yield to maturity? What is the yield to call? b. If you bought this bond, which return would you actually earn? Explain your reasoning. c. Suppose the bond had been selling at a discount rather than a premium. Would the yield to maturity have been the most likely return, or would the yield to call have been most likely? A: YTM): With a financial calculator, input N = 28, PV = -1165.75, PMT = 95, FV = 1000, I/YR = ? I/YR = YTM = 8.00%. (YTC): With a calculator, input N = 3, PV = -1165.75, PMT = 95, FV = 1090, I/YR = ? I/YR = YTC = 6.11%. b. Knowledgeable investors would expect the return to be closer to 6.1% than to 8%. If interest rates remain substantially lower than 9.5%, the company can be expected to call the issue at the call date and to refund it with an issue having a coupon rate lower than 9.5%. c. If the bond had sold at a discount, this would imply that current interest rates are above the coupon rate (i.e., interest rates have risen). Therefore, the company would not call the bonds, so the YTM would be more relevant than the YTC. PRICE AND YIELD An 8% semiannual coupon bond matures in 5 years. The bond has a face value of $1,000 and a current yield of 8.21%. What are the bond’s price and YTM? (Hint: Refer to Footnote 8 for the definition of the current yield and to Table 7-1.) A: N = 5 2 = 10, PMT = 80/2 = 40, and FV = 1000. In order to solve for I/YR we need PV. However, you are also given that the current yield is equal to 8.21%. Given this information, we can find PV (Price). Current yield = Annual interest/Current price 0.0821 = $80/PV PV = $80/0.0821 = $974.42. N = 10, PV = -974.42, PMT = 40, and FV = 1000. Solve for I/YR = YTM = 4.32%. However, this is a periodic rate so the nominal YTM = 4.32%(2) = 8.64%. Ch 8 PORTFOLIO BETA An individual has $35,000 invested in a stock with a beta of 0.8 and another $40,000 invested in a stock with a beta of 1.4. If these are the only two investments in her portfolios, what is her portfolio’s beta? A: Investment Beta $35,000 0.8 40,000 1.4 Total $75,000 bp = ($35,000/$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12.
REQUIRED RATE OF RETURN Assume that the risk-free rate is 6% and the expected return on the market is 13%. What is the required rate of return on a stock with a beta of 0.7? A: r = rRF + (rM – rRF)b = 6% + (13% – 6%)0.7 = 10.9%. EXPECTED AND REQUIRED RATES OF RETURN Assume that the risk-free rate is 5% and the market risk premium is 6%. What is the expected return for the overall stock market? What is the required rate of return on a stock with a beta of 1.2? A: rRF = 5%; RPM = 6%; rM = ? rM = 5% + (6%)1 = 11%. r when b = 1.2 = ? r = 5% + 6%(1.2) = 12.2%. BETA AND REQUIRED RATE OF RETURN A stock has a required return of 11%, the risk-free rate is 7%, and the market risk premium is 4%. a. What is the stock’s beta? b. If the market risk premium increased to 6%, what would happen to the stock’s required rate of return? Assume that the risk-free rate and the beta remain unchanged. A:a. r = 11%; rRF = 7%; RPM = 4%. r = rRF + (rM – rRF)b 11% = 7% + 4%b 4% = 4%b b = 1. b. rRF = 7%; RPM = 6%; b = 1. r = rRF + (rM – rRF)b = 7% + (6%)1 = 13%.